On mean waiting time completeness and equivalence of EDD and HOL-PJ dynamic priority in 2-class M/G/1 queue

This paper identifies two different parametrized dynamic priority queue disciplines, earliest due date (EDD) based and head of line priority jump (HOL-PJ), which are found to be mean waiting time complete in two class M/G/1 queue. An explicit one-to-one non linear transformation is obtained between earliest due date and delay dependent priority policy. Mean waiting time equivalence between these queue disciplines is established. Motivation behind the mean completeness and equivalence results is discussed from optimal control perspective. Notion of minmax fairness is introduced and it is argued that a simple global FCFS policy is the only solution for minmax fairness problem in two class by exploiting completeness in the structure of EDD based dynamic priority. Further, these completeness results are used to propose a simpler way for developing optimal control policy in celebrated c/ρ rule for two class M/G/1 queues.